In a test an examiner either guesses or copies or knows the answer to a multiple choice question with 4 choices. The probability that he/she makes a guess is 1 3 . The probability that he/she copies the answer is 1 6 . If the probability that the answer is correct, given that he/she copied it is 1 8 , then the probability that he/she knows the answer to a question given that he/she correctly answered it, is

Step-by-step solution

Let A be the event that the examinee gives the correct answer. Let G ,   C ,   K stand for guessing, copying and knowing. respectively. Given, P C = 1 6 ,   P G = 1 3 and P A C = 1 8 ⇒ P C + P G + P K = 1 ⇒ 1 6 + 1 3 + P K = 1 ∴   P K = 1 2 Also, P A K = 1 , for if the examinee knows, he/she will correctly answer it and P A G = 1 4 , since there are four choices. Now, total probability P A = P G P A G + P C P A C + P K P A K = 1 3 · 1 4 + 1 6 · 1 8 + 1 2 · 1 = 1